Modeling unsignalizedintersections at macroscopic
and micrsocopic scales:issues and proposals
Estelle CHEVALLIERLudovic LECLERCQ
LICIT, Laboratoire Ingénierie Circulation Transport(INRETS/ENTPE)
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. freecong.free cong.
Congested
no respect of the give-wayrule (Troutbeck, 2002)
alternating behaviourbetween both streams(Cassidy and Ahn, 2005)
On-field data Free-flow
search for acceptableheadways
gap-acceptance theoryGrabe (1954), Harders (1968),
Siegloch (1973)
supply-demand frameworkDaganzo (1995), Lebacque (1996, 2003),
Jin and Zhang (2003)
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. freecong.free cong.
Reference outputs for evaluation
Goal:
outputs of thereference models
outputs of simulation models
free-flowcongestion
macroscopicmicroscopic
Choice of the outputs: steady-state level
capacity curve:
dynamic level dynamic flow allocation:
delays:
( )
( )
1 2 1 2
1 1 2 2 1 2
, ( , )
( , ), ( , )
q q !
! !
= " "
= " " " "
1 2( , )d ! !
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. freecong.free cong.
Reference model in free-flow regime
insertion rules no. of insertions within a headway t: g(t)
capacity curve:
dynamic capacity allocation:
priority to major road
headway distribution: f(t)
delay formula: accounting for randomness in arrivalsand service times
GAP-ACCEPTANCE MODEL
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free cong. free cong.Reference models
cong. freeMicroscopic models Macroscopic models Conclusion
Reference model in congestion
priority ratio γ optimization in capacity (Ω) allocation
capacity curve:
dynamic capacity allocation:
shared priority/priority to minorroad
delay formula: deterministic arrivals and servicetimes
DEMAND-SUPPLY FRAMEWORK
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. freecong.free cong.
Goals of this study
Daganzo’s model(1995)
no insertion when Ωtoo lowq1/q2 not constant
congested:demand-supply
no delay whenΔ2<C(Δ1)no dynamics inqueue length
classicalmicroscopic models
free-flow:gap-acceptance
macroscopicmicroscopic
Simulation toolsBenchmark
models
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free cong. free cong. cong. freeReference models Microscopic models Macroscopic models Conclusion
MICROSCOPIC SIMULATION MODELS
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free cong. free cong. cong. freeReference models Microscopic models Macroscopic models Conclusion
Issues in free-flow
Simulation time-step ∆t = scanning frequency
inconsistentcapacity estimates!
capacity estimates independent on ∆t
simulated capacity and delays inagreement with the benchmark model
Assessing insertion rules within ∆t: as done in classicalmicroscopic models
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Issues in congestion
simulation time-step numerical viscosity
errors in vehicle’s trajectories
errors in the insertion decision process
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Issues in congestion
interactionscar-following/insertion rules
minimum values fordistance criteria
no insertion when theequilibrium spacing too short
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Issues in congestion
q1/q2 depends on ∆t lack of available spacingswhen Ω decreases
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Proposal for a solution
Decorrelation between the car-following algorithm and theinsertion rules Bernoulli process at each ∆t of probability: Φ2(∆1,∆2) ∆t relaxation model (Laval and Leclercq, 07; Cohen,04)
q1/q2 independent on ∆t insertion even if short spacings
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
MACROSCOPIC SIMULATION MODELS
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
In congestion
In macroscopic models: easy to implement the demand-supply framework through a distribution scheme
Daganzo’s model (1995): well adapted! invariance principle (Lebacque and Khoshyaran, 1996) capacity sharing
simulated capacity and delays in agreement with thebenchmark model
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Issues in free-flow
Stochastic interactions between vehicles are not takeninto account
no delay
accurate average delaybut no dynamics in queue length
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Proposal for a solution
Modeling the average effects of a stochastic gap-acceptance process through a fictive trafic light(Chevallier and Leclercq, 2007)
average period available for insertion=green average period of blocks=red
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Results
simulated capacity over a fictive cyclelength:
relevant with the benchmark model
simulated delays/ queue lengths:relevant with thebenchmark model
Δ2>C(Δ1)
Δ2≤C(Δ1)
classical macroscopic proposal
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
CONCLUSIONS
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Reference models Macroscopic models ConclusionMicroscopic modelsfree cong. cong. freefree cong.
Goals of this study
Daganzo’s model(1995)
congested:demand-supply
classical microscopicmodels
free-flow:gap-acceptance
macroscopicmicroscopic
Simulation toolsBenchmark
models
release interactions:car-following/insertion
average period of block due to
stochastic arrivals
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